Method of transmitting using phase shift-based precoding and an apparatus for implementing the same in a wireless communication system

ABSTRACT

A method of transmitting data using a plurality of subcarriers in a multi-antenna wireless communication system is disclosed. More specifically, the method includes receiving feedback information from a mobile station (MS), performing channel encoding and modulation independently on user data to be transmitted by each antenna using the received feedback information, determining a phase shift-based precoding matrix for increasing a phase angle of the user data by a fixed amount, and performing precoding using the determined phase shift-based precoding matrix on the user data.

This application is a divisional application of U.S. application Ser.No. 12/970,168, filed Dec. 16, 2010, which is a continuation of U.S.application Ser. No. 11/858,082, filed Sep. 19, 2007, which claims thebenefit of and right of priority to Korean Application No. P2007-003281,filed on Jan. 11, 2007, which are hereby incorporated by reference intheir entireties.

In addition, U.S. application Ser. No. 11/858/082 claims the benefit ofand right of priority to U.S. Provisional Application No. 60/826,143,filed on Sep. 19, 2006, which is hereby incorporated by reference in itsentirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of transmitting, and moreparticularly, to a method of transmitting using phase shift-basedprecoding and an apparatus for implementing the same in a wirelesscommunication system.

2. Discussion of the Related Art

With respect to wideband code division multiple access (W-CDMA) systems,researches are being conducted using a multiple antennas to increasesystem capacity, transmit speed of data, and link reliability by wayimplementing various schemes such as beamforming, multi-input,multi-output (MIMO), and transmit diversity. In particular, the MIMOscheme promotes high speed transmission via spatial diversity, similarto V-BLAST, is adopted in a 3^(rd) Generation Partnership Project(3GPP).

Furthermore, the two (2) antenna system adopted in Release 99 andRelease 4, based on transmit diversity, has been improved to a new typeof diversity scheme, such as a per antenna rate control (PARC) or a peruser unitary rate control (PU2RC), which considers operation using morethan three (3) antennas.

FIG. 1A is an exemplary diagram illustrating a structure of a PARC for asingle user. FIG. 1B is an exemplary diagram illustrating a structure ofa PARC for multiple users.

With respect to conventional V-BLAST, each transmit antenna can beconfigured using the same modulation and encoding without feedbackinformation from channel quality information (CQI). However, as shown inFIGS. 1A and 1B, the PARC uses the feedback information regarding thechannel conditions, such as a modulation coding set (MCS) and/or atransmit antenna subset (TAS), and selects the user data stream to betransmitted by each antenna.

Referring to FIG. 1A, any one of the three (3) user data streams isselected since this is an exemplary illustration the PARC for singleuser. Referring FIG. 1B, at least two (2) of the three (3) user datastreams are selected since this is an exemplary illustration the PARCfor multiple users.

Thereafter, the modulation and encoding using the feedback informationregarding the channel conditions is applied to the user data streamsstored in the buffer after being demultiplexed. The user data streamsare then multiplexed using a scheme (e.g., orthogonal frequency divisionmultiple access (OFDMA)) and transmitted via each antenna.

In other words, a base station (BS) applying the PARC scheme uses thefeedback information transmitted from a mobile station (MS) to performscheduling for optimizing transmission rate. Through this, one MS or twoor more MSs can simultaneously share frequency and time resources in thespace domain. Moreover, the PARC scheme allows for increase in diversitygain as a number of MSs scheduled by the BS increases.

By using the PARC scheme, the feedback overhead is reduced since onlythe CQI is used as the feedback information. With smaller or reducedoverhead, there is relatively less possibility of error during thefeedback process, and switching can take place between the PARC for thesingle user and the PARC for the multiple users. However, in case of thePARC for multiple users, interference between users can occur thusaffecting transmission efficiency.

FIG. 2 is an exemplary diagram illustrating a structure of a PU2RC. ThePU2RC uses spatial multiplexing for transmitting data streams ofmultiple users. As such, multiple data streams are selected fortransmission to multiple users. In the PU2RC, a unitary matrix based ona singular value decomposition of the MIMO channel is used to performprecoding.

More specifically, the unitary matrix in a transmitter is a set ofunitary basic vectors selected by all users (or MSs). If the set ofvectors is fixed, represented by M, the unitary basic vectors areselected by one or multiple users.

Furthermore, the PU2RC can be used to reduce inter-user interference andachieve high efficiency gain. However, the feedback information size canbe large since information can include preferred matrix index inaddition preferred vector in the matrix, thus increasing the possibilityof transmission error due to the large size of the feedback information

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a method oftransmitting using phase shift-based precoding and an apparatus forimplementing the same in a wireless communication system thatsubstantially obviates one or more problems due to limitations anddisadvantages of the related art.

An object of the present invention is to provide a method oftransmitting data using a plurality of subcarriers in a multi-antennawireless communication system.

Another object of the present invention is to provide a transmitting andreceiving device in a multi-user, multi-antenna communication systemusing a plurality of subcarriers.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objectives and other advantages of the invention may berealized and attained by the structure particularly pointed out in thewritten description and claims hereof as well as the appended drawings.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein, amethod of transmitting data using a plurality of subcarriers in amulti-antenna wireless communication system includes receiving feedbackinformation from a mobile station (MS), performing channel encoding andmodulation independently on user data to be transmitted by each antennausing the received feedback information, determining a phase shift-basedprecoding matrix for increasing a phase angle of the user data by afixed amount, and performing precoding using the determined phaseshift-based precoding matrix on the user data.

In another aspect of the present invention, a transmitting and receivingdevice in a multi-user, multi-antenna communication system using aplurality of subcarriers includes a channel encoder and modulatorconfigured to perform channel coding and modulation independently onuser data for each antenna using feedback information from the receivingdevice, and a first precoder configured to determine a phase shift-basedprecoding matrix and to perform precoding on the user data using thedetermined phase shift-based precoding matrix, wherein the phaseshift-based precoding matrix is determined based on increasing a phaseangle of the user data for each antenna fixedly.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this application, illustrate embodiment(s) of the invention andtogether with the description serve to explain the principle of theinvention. In the drawings;

FIG. 1A is an exemplary diagram illustrating a structure of a PARC for asingle user, and FIG. 1B is an exemplary diagram illustrating astructure of a PARC for multiple users;

FIG. 2 is an exemplary diagram illustrating a structure of a PU2RC;

FIG. 3A is an exemplary diagram illustrating a transmitter of acommunication system according to Embodiment #1;

FIGS. 3B and 3C are exemplary diagrams illustrating processes orprocedures of the precoder of the transmitter of FIG. 3A;

FIG. 4 is an exemplary diagram illustrating phase shift-based precoding;

FIG. 5 is an exemplary diagram illustrating change in channel size as aresult of cyclic delay;

FIG. 6 is an exemplary diagram illustrating a multiple antenna system,having four (4) transmit antennas and the spatial multiplexing rate of2, to which a conventional spatial multiplexing and cyclic delaydiversity schemes are applied;

FIG. 7 is an exemplary diagram of a multiple antenna system to which thephase shift-based precoding matrix of Equation 10 is applied;

FIG. 8 is an exemplary diagram of a four-antenna system where a specificpart of the precoding matrix is selected;

FIG. 9 is an exemplary diagram illustrating a transmitter according tothe Embodiment #2;

FIG. 10 is an exemplary diagram illustrating a process of a transmitterand a receiver in a multi-antenna system which supports codebook-basedprecoding;

FIG. 11A is an exemplary diagram illustrating a comparison between aconventional PARC and the method of the present invention in anenvironment where there is no spatial correlation in an ITU PedAchannel;

FIG. 11B is an exemplary diagram illustrating a comparison between aconventional PARC and the method of the present invention in anenvironment where the spatial correlation is 70%;

FIG. 12A is an exemplary diagram illustrating a comparison between aconventional PARC and the method of the present invention in a TUchannel having high frequency selection; and

FIG. 12B is another exemplary diagram illustrating a comparison betweena conventional PARC and the method of the present invention in a TUchannel having high frequency selection.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

The discussions related to the present invention can be applied invarious wireless communication systems. The wireless communicationsystem can be used to provide services related to voice, audio, packetdata, etc. Moreover, the discussions to follow can be used in downlinkas well as uplink transmissions. Here, the downlink transmission refersto transmission from a BS to a MS, and conversely, the uplinktransmission refers to transmission from the MS to the BS.

The BS can be generally referred to a fixed station and can also bereferred to as Node B, a base transceiver system (BTS), an access point(AP), a network, and a serving station, among other names. The MS can bemobile and/or fixed and can be referred to as a user equipment (UE), auser terminal (UT), a subscriber station (SS), a mobile subscriberstation (MSS), a mobile terminal (MT), and a wireless device, amongother names.

The discussions related to the present invention can be applied to asingle carrier or a multi-carrier communication system. A multi-carriersystem can use various modulation schemes, such as an orthogonalfrequency division multiplexing (OFDM) and an orthogonal frequencydivision multiple access (OFDMA). The OFDM/OFDMA is a scheme in whichthe bandwidths of the entire system are partitioned into a plurality ofsubcarriers having orthogonality. Here, the subcarriers can also bereferred to as a subband or a tone. Alternatively, the single-carriersystem can use various modulation schemes including a single-carrierfrequency division multiple access (SC-CDMA) or a code division multipleaccess (CDMA).

Generally, a communication system comprises a transmitter and areceiver. Here, a unit or a module which can perform the functions ofthe transmitter and the receiver can be referred to as a transceiver.However, for the purpose of discussing feedback information, thetransmitter and the receiver can be independently used.

In the downlink direction, the transmitter can be a part of the BS, andthe receiver can be a part of the MS. Alternatively, the transmitter canbe a part of the MS while the receiver can be a part of the BS. The BScan include a plurality of transmitters and/or receivers. Similarly, theMS can include a plurality of transmitters and/or receivers.

Embodiment #1

This embodiment relates to optimizing the transmission efficiency byindependently configuring modulation and encoding of each transmissionantenna in a multi-user, multi-antenna system. Here, a phase shift-basedprecoding can be applied to minimize or reduce interference betweenusers.

FIG. 3A is an exemplary diagram illustrating a transmitter of acommunication system according to Embodiment #1. Referring to FIG. 3A,the transmitter 100 comprises a scheduler/multiplexer 110, a pluralityof channel encoders/modulators (120-1˜120-N), a precoder 130, aplurality of serial/parallel (SP) converters (140-1˜140-N_(t)), aplurality of modulators (150-1˜150-N_(t)).

FIGS. 3B and 3C are exemplary diagrams illustrating processes orprocedures of the precoder of the transmitter of FIG. 3A.

In FIG. 3A, the scheduler/multiplexer 110 can be configured to schedulethe user (or the MS) when the streams of information bits are inputtedby each user. From the scheduled users, the actual user for transmissioncan be selected, and the selected information bits can be multiplexed.

The plurality of channel encoders/modulators (120-1˜120-N) can beconfigured to output coded data by encoding the multiplexed informationbits according to a prescribed coding scheme(s). Thereafter, the codeddata can be modulated using a prescribed modulation scheme. Theinformation bits can include text, audio, video, or other types of data.

Furthermore, the plurality of channel encoders/modulators (120-1˜120-N)can attach or add an error detection bits (e.g., cyclic redundancy check(CRC)) to the information bits and further add extra codes for errorcorrection. The error correction codes include a turbo code, a lowdensity parity check code (LDPC), and a convolution code, among othervarious error correction codes.

The plurality of channel encoders/modulators (120-1˜120-N) can beconfigured to map (or allocate) the coded data to symbols on anamplitude and phase constellation. The modulation schemes that can beapplied are not limited and can vary, and these schemes can be anm-quadrature phase shift keying (m-PSK) scheme or a m-quadratureamplitude modulation (m-QAM) scheme. For example, the m-PSK schemeincludes a binary phase shift keying (BPSK), a quadrature phase shiftkeying (QPSK), or an 8-PSK. Moreover, the m-QAM includes a 16-QAM, a64-QAM, or a 256-QAM.

The precoder 130 can be configured to apply phase shift-based precodingto the mapped symbols. Here, the precoder 130 can output a transmitsymbol which is a set of symbols transmitted during one transmissionperiod or one time slot. The details of the phase shift-based precodingperformed by the precoder 130 will be discussed later.

The plurality of S/P converters (140-1˜140-N_(t)) can be configured tooutput the precoded transmit symbols in parallel to the plurality ofmodulators (150-1˜150-N_(t)). The plurality of modulators(150-1˜150-N_(t)) can be configured to modulate each transmit symbolsfrom the S/P converters (140-1˜140-N_(t)) according to a multiple accessmodulation scheme. The multiple access modulation schemes that can beapplied are not limited, and these schemes can be a single-carriermodulation scheme (e.g., CDMA) or a multi-carrier modulation scheme(e.g., OFDMA).

Discussed below is a phase shift-based precoding scheme applied in atwo-antenna system and/or a four-antenna system using OFDM multi-carriermodulation scheme. Further, the discussions relate to application of thephase shift-based precoding to a multi-antenna system having N_(t)number of antennas. More specifically, the discussions may be based on astructure of a generalized phase shift-based precoding matrix which canbe applied to enhancing the multi-antenna system having N_(t) number ofantennas.

Phase Shift-Based Precoding Scheme

FIG. 4 is an exemplary diagram illustrating phase shift-based precoding.The phase shift-based precoding can be defined as a scheme by which thedata streams are transmitted via all the antennas but with different (orindependent) phase sequence multiplied thereto. Generally, if a smallcyclic delay can be used to generate a phase sequence, a frequencyselection of a channel is provided from the perspective of the receiver(e.g., MS), and the size of the channel can increase or decreasedepending on the frequency domain.

FIG. 5 is an exemplary diagram illustrating change in channel size as aresult of cyclic delay. Referring to FIG. 5, the transmitter 100 canachieve frequency diversity by allocating users (or MSs) to parts of thefrequency whose channel condition improves due to increase in frequencyof the frequency domain. Here, certain parts of the frequency domain hasa large frequency bandwidth and is less affected by fluctuations causedby relative small cyclic delay values. In order to apply cyclic delayvalues which increases or decreases uniformly to each antenna, the phaseshift-based precoding matrix, P, can be used as expressed as in Equation1.

$\begin{matrix}{P_{N_{t} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & \ddots & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

Referring to Equation 1, k denotes index of subcarriers or frequencyresource index in which a specific frequency bandwidth is allocated foreach resource, and

w^(k) _(i,j)(i=1. . . , N_(t), j=1, 1, . . . , R) denotes a complexweight determined according to k. Moreover, N_(t) denotes a number oftransmit antennas or virtual antennas (e.g., a number of spatialmultiplexing rate) while R denotes spatial multiplexing rate. Here, thecomplex weight value can be variable according to the index of the OFDMsymbols and corresponding subcarriers multiplied to antennas. Inaddition, the complex weight value can be determined by channelcondition and/or feedback information. Preferably, the precoding matrix,P, of Equation 1 is configured using a unitary matrix so as to reduceloss in channel capacity of a multi-antenna system.

The following equation can be used to express a channel capacity of amulti-antenna open-loop system so as to define the elements (orcomponents) of the unitary matrix.

$\begin{matrix}{{{Cu}(H)} = {\log_{2}\left( {\det \left( {I_{N_{r}} + {\frac{SNR}{N}{HH}^{H}}} \right)} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

Referring to Equation 2, H denotes a multi-antenna channel matrix havinga size of N_(r)×N_(t), and N_(r) denotes a number of receiving antennas.If Equation 2 is applied to the phase shift-based precoding matrix P,the result can be expressed as shown in Equation 3.

$\begin{matrix}{C_{precoding} = {\log_{2}\left( {\det \left( {I_{N_{r}} + {\frac{S\; N\; R}{N}{HPP}^{H}H^{H}}} \right)} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

Referring to Equation 3, in order to minimize or eliminate channelcapacity loss, PP^(H) must be an identity matrix. As such, the phaseshift-based matrix P has to satisfy the following condition of Equation4.

PP^(H)=I_(N)   [Equation 4]

In order for the phase shift-based precoding matrix P to be converted toan identity matrix, two (2) conditions need to be satisfied. That is, apower limitation condition and orthogonality limitation condition needto be met simultaneously. The power limitation condition relates tomaking the size of each column of the matrix to equal 1. Moreover, theorthogonality limitation condition relates to making each columnorthogonal (or the columns are orthogonal to each other). Equation 5 andEquation 6 are examples of these.

$\begin{matrix}{{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},{{{w_{1,2}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},\vdots}{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \\{{{{{w_{1,1}^{k^{*}}w_{1,2}^{k}} + {w_{2,1}^{k^{*}}w_{2,2}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},2}^{k}}} = 0},{{{w_{1,1}^{k^{*}}w_{1,3}^{k}} + {w_{2,1}^{k^{*}}w_{2,3}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},3}^{k}}} = 0},\vdots}{{{w_{1,1}^{k^{*}}w_{1,R}^{k}} + {w_{2,1}^{k^{*}}w_{2,R}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},R}^{k}}} = 0}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

The discussions above with respect to Equations 2-6 relate to a unitarymatrix. Hereafter, the discussions of the unitary matrix relate to aphase shift-based precoding matrix having a 2×2 matrix size.

Equation 7 represents a general phase shift-based precoding matrixapplied in a system having a spatial multiplexing rate of 2 and two (2)transmit antennas.

$\begin{matrix}{P_{2 \times 2}^{k} = \begin{pmatrix}{\alpha_{1}^{j\; k\; \theta_{1}}} & {\beta_{1}^{j\; k\; \theta_{2}}} \\{\beta_{2}^{j\; k\; \theta_{3}}} & {\alpha_{2}^{j\; k\; \theta_{4}}}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Referring to Equation 7, α_(i),β_(i)(i=1, 2) represents real numbers,0_(i) (i=1, 2, 3, 4) denotes a phase value, and k denotes subcarrierindex or resource index of OFDM signals.

In order to convert such a precoding matrix (e.g., Equation 7) into aunit matrix, the power limitation condition of Equation 8 and theorthogonality limitation condition of Equation 9 need to be satisfied.

$\begin{matrix}{{{{{a_{1}^{{jk\theta}_{1}}}}^{2} + {{\beta_{2}^{{jk\theta}_{3}}}}^{2}} = 1},{{{{a_{2}^{{jk\theta}_{4}}}}^{2} + {{\beta_{1}^{{jk\theta}_{2}}}}^{2}} = 1}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \\{{\left( {a_{1}^{{jk\theta}_{1}}} \right)^{*} + {\beta_{1}^{{jk\theta}_{2}}}} = {{1 + \left( {\beta_{2}^{{jk\theta}_{3}}} \right)^{*} + {a_{2}^{{jk\theta}_{4}}}} = 0}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

In Equations 8 and 9, * denotes a conjugate complex number. If the phaseshift-based precoding matrix having a size of 2×2 satisfies Equations7-9, such a matrix can be expressed as follows as shown in Equation 10.

$\begin{matrix}{P_{2 \times 2}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & ^{j\; k\; \theta_{2}} \\^{j\; k\; \theta_{3}} & 1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

Referring to Equation 10, θ₂ and θ₃ maintain an orthogonal relationshipbased on satisfying the orthogonality limitation condition. This can beexpressed as shown in Equation 11.

kθ ₃ =−kθ ₂+π  [Equation 11]

The precoding matrix can be stored in the transmitter and the receiverin a form of a codebook. The codebook can include various precodingmatrix generated using a specified number of different θ₂ values. Here,θ₂ value can be configured based on the channel conditions and whetherfeedback information is provided or not. If the feedback information isprovided (or used), θ₂ value can be configured to be a small value. Ifthe feedback information is not provided (or not used), θ₂ value can beconfigured to be a large value so as to attain high frequency diversitygain.

Even if the phase shift-based matrix is generated, similar to Equation7, the multiplexing rate R may have to be set low in view of actualnumber of antennas due to the channel condition. In such a case, aspecified number of columns corresponding to a current spatialmultiplexing rate (e.g., reduced spatial multiplexing rate) from thegenerated phase shift-based precoding matrix can be selected toreconfigure the phase shift-based precoding matrix. In other words, anew precoding matrix to be applied to the corresponding system is notgenerated each time the spatial multiplexing rate is changed. Rather,the initial (or first generated) phase shift-based precoding matrix cancontinue to be used, and a specified column of the correspondingprecoding matrix can be selected to reconfigure the precoding matrix.

For example, referring to Equation 10, the multi-antenna communicationsystem comprises two (2) transmit antennas, and the spatial multiplexingrate is 2. However, the spatial multiplexing rate can change and can bereduced to 1. In such a case, a column from the precoding matrix ofEquation 10 can be selected and the selected column can be used forprecoding.

For example, if a second column is selected, the phase shift-basedprecoding matrix can be expressed as shown in Equation 12. Moreover,this form of equation is analogous to the form where cyclic delaydiversity scheme is applied in a two (2) transmit antenna system.

$\begin{matrix}{P_{2 \times 1}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}^{j\; k\; \theta_{2}} \\1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Equation 12 an exemplary illustration associated with a system havingtwo (2) transmit antennas. However, this equation can also be applied toa system having four (4) transmit antennas. In other words, in a four(4) transmit antenna system, after the phase shift-based precodingmatrix is generated, a specified column can be selected in accordancewith the changing spatial multiplexing rate (e.g., spatial multiplexingrate from 2 to 1), and the selected specified column can be used forprecoding.

FIG. 6 is an exemplary diagram illustrating a multiple antenna system,having four (4) transmit antennas and the spatial multiplexing rate of2, to which a conventional spatial multiplexing and cyclic delaydiversity schemes are applied. FIG. 7 is an exemplary diagram of amultiple antenna system to which the phase shift-based precoding matrixof Equation 10 is applied.

Referring to FIG. 6, a first sequence S₁ and a second sequence S₂ aresent to a first antenna (e.g., ANT #1) and a third antenna (e.g., ANT#3), respectively. Moreover, a phase shifted first sequence (s₁e^(jθ) ¹) and a phase shifted second sequence (s₂e^(jθ) ¹ ) are sent to a secondantenna (e.g., ANT #2) and a fourth antenna (e.g., ANT #4),respectively. Based on such arrangement, it is evident that the spatialmultiplexing rate is 2.

Referring to FIG. 7, a sequence s₁+s₂e^(jkθ) ² is sent to the firstantenna (e.g., ANT #1), a sequence s₁e^(jkθ) ³ +s₂ is sent to the thirdantenna (e.g., ANT #3), a sequence s₁e^(jkθ) ¹ +s₂e^(jk(θ) ¹ ^(+θ) ² ⁾is sent to the second antenna (e.g., ANT #2), and a sequence s₁e^(jk(θ)¹ ^(+θ) ¹ ⁾ s₂e^(jkθ) ¹ is sent to the fourth antenna (e.g., ANT #4).

Compared to the system of FIG. 6, the system of FIG. 7 uses a unitaryprecoding matrix to perform cyclic delay (or phase shift) on four (4)antennas so as to take advantage of the cyclic delay diversity scheme.

The phase shift-based precoding matrix per spatial multiplexing rate ina two (2) antenna system and a four (4) antenna system can be organizedas follows.

TABLE 1 Two-Antenna System Four-Antenna System Spatial MultiplexingSpatial Multiplexing Spatial Multiplexing Spatial Multiplexing Rate 1Rate 2 Rate 1 Rate 2 $\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\e^{j\; \theta_{1}k}\end{pmatrix}$ $\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {- e^{{- j}\; \theta_{1}k}} \\e^{j\; \theta_{1}k} & 1\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 \\e^{j\; \theta_{1}k} \\e^{j\; \theta_{2}k} \\e^{j\; \theta_{3}k}\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- e^{{- j}\; \theta_{1}k}} \\e^{j\; \theta_{1}k} & 1 \\e^{j\; \theta_{2}k} & {- e^{{- j}\; \theta_{3}k}} \\e^{j\; \theta_{3}k} & {- e^{{- j}\; \theta_{2}k}}\end{pmatrix}$

Referring to Table 1, θ_(i)(i=1, 2, 3) denotes cyclic delay valuesaccording to the phase angles, and k denotes an index of OFDMsubcarriers or resource index. Each of the four (4) types of precodingmatrices shown in Table 1 can be acquired by selecting a specific partof the precoding matrix from the four (4) antenna system having thespatial multiplexing rate of 2. This is illustrated in FIG. 8 which isan exemplary diagram of a four-antenna system where a specific part ofthe precoding matrix is selected.

In addition, the storage or memory of the transmitter and the receivercan be conserved since each of the four (4) precoding matrix, as shownin Table 1, does not need to be separately or independently provided inthe codebook. Further, the phase shift-based precoding matrix, asdiscussed above, can be applied to a system having M number of antennaswith the multiplexing rate of N (N≦M) based on the same logic.

A First Precoder for Implementing Phase Shift-Based Precoding Scheme

The first precoder 130 comprises a precoding matrix generation module131-1, a matrix reconfiguration module 133-1, and a precoding module134-1. More specifically, the precoding matrix generation module 131-1can be configured to determine a reference row corresponding to a firstsubcarrier from a prescribed precoding matrix, and to perform phaseshift to determine remaining rows. Here, phase shifting is based onincreasing the phase angle of the reference row by a constant or uniformamount.

In the present invention, the precoding can be performed using a unitarymatrix having a specified size (e.g., (number of transmitantennas)×(spatial multiplexing rate)). The unitary matrix can beprovided to index of each subcarrier or index resource, and the unitarymatrix for the first index can be phase shifted so that the unitarymatrix for the rest of the indices can be determined

The precoding matrix generation module 131-1 can select an arbitraryfirst precoding matrix from the codebook stored in the memory. Thesecond precoding matrix for the subcarriers of the second index can begenerated by applying a small phase shift to the first precoding matrix.Here, the amount of phase shift can be determined based on the channelcondition and/or whether feedback information is received or not.

Moreover, the third precoding matrix for the subcarriers of the thirdindex can be generated by applying a small phase shift to the secondprecoding matrix. Similarly, the rest of the precoding matrices up tothe last precoding matrix can be generated according to the processesdescribed above.

The matrix reconfiguration module 133-1 can be configured to select aspecified number of columns corresponding to the spatial multiplexingrate (e.g., 1 or 2) of each precoding matrix generated from theprecoding matrix generation module 131-1, and to discard remaining (ornon-selected) columns in reconfiguring the precoding matrix. Here,precoding matrix can be generated based on only the selected column.Furthermore, an arbitrary column can be selected as the specified columnfrom the precoding matrix, or the specific column can be selectedaccording to a prescribed scheme.

Lastly, the precoding module 134-1 can be configured to performprecoding by substituting or assigning OFDM symbols corresponding to thesubcarriers to each of the determined precoding matrix.

A Generalized Phase Shift-Based Precoding Scheme

The discussion of above with respect to configuring a phase shift-basedprecoding matrix was based on a system having four (4) transmit antennasand a spatial multiplexing rate or 2. As mentioned above, the discussionof above can also be applied to a system having N_(t) number of antennas(N₁ greater than or equal to 2 and is a natural number) and the spatialmultiplexing rate is R (R>1 and is a natural number). Such anapplication can be implemented using the processes described above orcan generalized using Equation 13.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}^{j\; \theta_{1}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & ^{j\; \theta_{N_{t}}k}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Referring to Equation 13, the matrix to the right of the equal sign(‘=’) represents a unitary matrix for phase shift, and the matrix U is aunitary matrix for a specific purpose which satisfies

_(N) _(t) _(×R) ^(H)×

_(n) _(t) _(×R)=

_(R×R).

Further, if a system has two (2) transmit antennas and uses a 1-bitcodebook, the phase shift-based precoding matrix can be expressed asshown in Equation 14.

Referring to Equation 14, since β can be determined relatively easilyonce α is determined, α can be pre-set with two (2) values and theinformation regarding the pre-set values can be fed back in form ofcodebook index. For example, if the feedback codebook index is 0, α canbe 0.2, and if the feedback codebook index is 1, then α can be 0.8. Suchvalues can be predetermined and shared between the transmitter and thereceiver. In addition, each column can be allocated to differentuser(s).

As an example of the matrix U, a prescribed precoding matrix can be usedto achieve signal-to-noise (SNR) diversity gain. To this end, if a Walshcode is used, the phase shift-based precoding matrix P can be expressedas shown in Equation 15.

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}^{j\; \theta_{1}k} & 0 & 0 & 0 \\0 & ^{j\; \theta_{2}k} & 0 & 0 \\0 & 0 & ^{j\; \theta_{3}k} & 0 \\0 & 0 & 0 & ^{j\; \theta_{4}k}\end{pmatrix}\begin{pmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

Referring to Equation 15, this is based on a system having four (4)transmit antennas and a spatial multiplexing rate of 4. Here, the secondmatrix to the right of the equal sign (e.g., represented in 1s and −1s)can be reconfigured to select a specific antenna (e.g., antennaselection) and/or adjust spatial multiplexing rate (e.g., rate tuning)

Equation 16 represents reconfigured unit matrix for selecting two (2)antennas in a system having four (4) transmit or virtual antennas.

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}^{j\; \theta_{1}k} & 0 & 0 & 0 \\0 & ^{j\; \theta_{2}k} & 0 & 0 \\0 & 0 & ^{j\; \theta_{3}k} & 0 \\0 & 0 & 0 & ^{j\; \theta_{4}k}\end{pmatrix}\begin{pmatrix}0 & 0 & 1 & 1 \\0 & 0 & 1 & {- 1} \\1 & 1 & 0 & 0 \\1 & {- 1} & 0 & 0\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

As discussed, the spatial multiplexing rate can change or vary due tovarious factors including affects in time and/or channel conditions. Thefollowing Table 2 shows a method for reconfiguring the second matrix tothe right of the equal sign (e.g., represented by 0s, 1s, and −1s) tocorrespond to the changed (or changing) spatial multiplexing rate.

TABLE 2

Referring to Table 2, the first column, the first and second columns,and/or first through fourth columns are selected according to themultiplexing rate (e.g., multiplexing rate of 1, 2, or 4). However, themultiplexing rate (or selection of columns) is not limited to theexample of Table 2, but the multiplexing rate can be one (1) and any oneof the four columns can be selected. Moreover, if the multiplexing rateis two (2), any two columns of the four columns (e.g., 1-2, 2-3, 3-4, or4-1) can be selected.

Further, one or more column(s) in the matrix in Table 2 can be allocatedto different user(s) in order to share spatial domain resource(s).

In addition, the second matrix can be provided to the transmitter andthe receiver in a form of a codebook. In such a case, the transmittercan receive the index information of the codebook from the receiver.Thereafter, the transmitter can select a unitary matrix (e.g., thesecond matrix) of the corresponding index from the codebook and useEquation 13 to configure the phase shift-based precoding matrix.

Furthermore, the cyclic delay value for phase shift-based precodingmatrix can be a value that is predetermined at the transmitter and thereceiver. Alternatively, this value can be a value that is provided tothe transmitter via the feedback information. Moreover, the spatialmultiplexing rate R can be a predetermined value at the transmitter andthe receiver. However, the spatial multiplexing rate R can be providedas feedback information by the receiver to the transmitter after thereceiver calculates the spatial multiplexing rate upon periodicallymeasuring the channel conditions. Here, the transmitter can use thechannel information fed back from the receiver to calculate and/ormanipulate the spatial multiplexing rate.

For additional description and/or more details regarding the discussionsrelated to the embodiments of the present invention, Korean ApplicationNo. 2006-97216, filed on Oct. 2, 2006, and Korean Application No.2007-37008, filed on Apr. 16, 2007, can be referred to, which are herebyincorporated by reference.

A First Precoder for Implementing a Generalized Phase Shift-BasedPrecoding Scheme

A first precoder 130 comprises a precoding matrix determining module131-2, an antenna selection module 132, a matrix reconfiguration module133-2, and a precoding module 134-2.

More specifically, the precoding matrix determining module 131-2 can beconfigured to determine a phase shift-based precoding matrix bymultiplying the second matrix which satisfies the conditions associatedwith the first matrix (e.g., Equation 13) and the unitary matrix.

The antenna selection module 132 can be configured to select at leastone partial matrix having a size of n×n (0<n<N) corresponding to aspecific antenna from the second matrix (e.g., Equation 16), and selecta specific antenna to be used for data transmission by configuring allelements other than the selected element to zero (0). Here, the selectedelement.

The matrix reconfiguration module 133-2 can be configured to select anumber of columns corresponding to the spatial multiplexing rate of thesecond matrix (e.g., Table 2) and to reconfigure the second matrix usingonly the selected columns.

Although not described above, there are other components of thetransmitter which may be necessary for operation. Such as, for example,a memory (not shown) can be used to store various information, areceiver circuit (not shown) can be used to receive feedbackinformation, and a controller (not shown) can be used to control variouscomponents of the transmitter.

In detail, the memory can store a codebook for the phase shift-basedprecoding matrix and/or a modulation and coding scheme (MCS) lookuptable for supporting adaptive channel coding and modulation (AMC)scheme. The codebook can include at least one item associated with thephase shift-based precoding matrix and at least one item associated witheach matrix index. Moreover, the MCS lookup table can include at leastone item associated with coding rate to be applied to the inputtedinformation bits, at least one item associated with modulation scheme,and at least one item associated with MCS level index.

The receiver circuit can receive the transmitted signals from thereceiver via the antenna, converts the received signals into digitalsignal, and send the digitally converted signals to the controller. Thereceived signals can include information such as channel qualityinformation (CQI). The CQI can be included in feedback information andcan be used to provide information related to channel condition, codingscheme(s), and/or modulation scheme(s). More specifically, the CQI canbe associated with index for the phase shift-based precoding matrix,index for a specific coding rate and/or modulation scheme or modulationsize. As index information, the MCS level index can be used.

Embodiment #2

In another embodiment of the present invention, precoding based on acodebook can be used to schedule transmit power more efficiently so asto increase transmit reliability as well as transmit throughput.Moreover, such a method can be implement in a transmitter and areceiver.

FIG. 9 is an exemplary diagram illustrating a transmitter according tothe Embodiment #2. Referring to Embodiment #1, the transmitter 100comprises a scheduler/multiplexer 110, a plurality of channelencoders/modulators (120-1˜120-N), a precoder 130, a plurality ofserial/parallel (SP) converters (140-1˜140-N_(t)), a plurality ofmodulators (150-1˜150-N_(t)).

Referring to FIG. 9, the transmitter 200 comprises ascheduler/multiplexer 210, a plurality of channel encoders/modulators(220-1˜220-N), a precoder 240, a plurality of serial/parallel (SP)converters (250-1˜250-N_(t)), a plurality of modulators(260-1˜260-N_(t)). In addition, a precoder based on codebook 230 isfurther included.

In order to distinguish codebook-based precoding performed by theprecoder 240 from the phase shift-based precoding performed by theprecoder 130 (referred to as Precoding #1), the codebook-based precodingwill be referred to as Precoding #2. Precoding #2 relates to a scheme bywhich SNR gain can be achieved by receiving as feedback from thereceiver an index of the precoding matrix, known to both the transmitterand the receiver.

FIG. 10 is an exemplary diagram illustrating a process of a transmitterand a receiver in a multi-antenna system which supports codebook-basedprecoding. Referring to FIG. 10, the transmitter and the receiver eachhave a fixed precoding matrix (P₁˜P_(L)). The receiver can use thechannel information to transmit as feedback to the transmitter anoptimum precoding matrix index 1. After receiving the feedbackinformation, the precoder 240 of the transmitter can then apply theprecoding matrix corresponding to the index to the transmit data(X₁˜X_(Mt)).

Table 3 shows an example of a codebook that can be applied in a systemhaving two (2) transmit antennas with the spatial multiplexing rate of2, and the system uses 3-bit feedback information.

TABLE 3 Matrix Index (binary) Column 1 Column 2 000 1    0      0   1      001 0.7940 −0.581 − j0.1818 −0.5801 + j0.1818   −0.7940 0100.7940 0.0576 − j0.6051 0.0576 + j0.6051 −0.7940 011 0.7941 −0.2978 +j0.5298   −0.2978 − j0.5298   −0.7941 100 0.7941 0.6038 − j0.06890.6038 + j0.0689 −0.7941 101 0.3289 0.6614 − j0.6740 0.6614 + j0.6740−0.3289 110 0.5112 0.4754 + j0.7160 0.4754 − j0.7160 −0.5112 111 0.3289−0.8779 + j0.3481   −0.8779 − j0.3481   −0.3289

If the codebook-based precoding and the phase shift-based precoding areapplied simultaneously, the transmitter can receive periodicallyinformation of the preferred precoding index of the receiver, the CQI,and the frequency bandwidth having the best or acceptable channelcondition. Having such feedback information as basis, the transmittercan use the same precoding index and can perform scheduling of preferreddata stream(s) to different receivers (e.g., MSs) on the same frequencyand the same time frame.

Furthermore, the memory (not shown) of Embodiment #2 can include morecodebooks for precoding compared to that of Embodiment #1. Moreover, thereceiver circuit (not shown) of Embodiment #2 can receive moreinformation associated with codebook index for selecting precodingmatrix from the codebook compared to that of Embodiment #1.

The transmitter and the receiver with respect to Embodiments #1 and #2can include an interleaver (not shown) for performing interleaving byparsing code bits so as to minimize loss caused by noise in transmittingdata. Moreover, an inverse fast Fourier transform (IFFT) (not shown) canbe included for allocating the precoded transmit symbols to thesubcarriers in the time domain. In addition, the transmitter and thereceiver with respect to Embodiments #1 and #2 can also include a filter(not shown) for converting the transmit symbols to high frequencysignals, and an analog converter (not shown).

Further, the following discussion relates to a simulation or a test thecapability of the phase shift-based precoding in a multi-user,multi-antenna system. Table 4 shows the results of the simulation or thetest.

TABLE 4 Parameter Configuration System Structure 3GPP LTE system(OFDMA-based downlink) OFDM Parameters 5 MHz (300 + 1 subcarriers)Subframe Length) 0.5 ms Resource Block Size) 75 subcarriers * 4 OFDMsymbol Channel Models ITU Pedestrian A, Typical Urban (6-ray) MobileSpeed (km/h) 3 Modulation Schemes and QPSK (R = 1/3, 1/2, 3/4) ChannelCoding Rates 16-QAM (R = 1/2, 5/8, 3/4) 64-QAM (R = 3/5, 2/3, 3/4, 5/6)Channel Code Turbo code Component decoder: max-log-MAP MIMO Mode MU-MIMOResource Allocation Localized mode Antenna Configuration [2Tx, 2Rx]Spatial Correlation (0%, 0%), (70%, 70%) (Tx, Rx) MIMO Receiver MMSEreceiver Channel Estimation Perfect channel estimation H-ARQ Bit-levelchase combining # of Maximum Retransmission: 3 TTIs # of Retransmissiondelay: 3 TTIs

FIG. 11A is an exemplary diagram illustrating a comparison between aconventional PARC and the method of the present invention in anenvironment where there is no spatial correlation in an ITU PedAchannel. FIG. 11B is an exemplary diagram illustrating a comparisonbetween a conventional PARC and the method of the present invention inan environment where the spatial correlation is 70%.

Referring to FIGS. 11A and 11B, the throughput according to the presentinvention is always higher than the transmit method of PARC, regardlessof the spatial correlation of the transmitter and the receiver.Furthermore, the difference is noticeably amplified as the spatialcorrelation of the transmitter and the receiver is increased. That is,the overall transmit capability is increased due to decrease inmulti-user interference.

FIG. 12A is an exemplary diagram illustrating a comparison between aconventional PARC and the method of the present invention in a TUchannel having high frequency selection. FIG. 12B is another exemplarydiagram illustrating a comparison between a conventional PARC and themethod of the present invention in a TU channel having high frequencyselection.

Referring to FIG. 12A, the difference is minimal between the PARC andthe present invention, regardless of the spatial correlation. In FIG.12B, with the spatial correlation of the transmitter and the receiver at70%, the throughput is increased by 15% as a result of SNR gain due tocodebook-based precoding.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the inventions. Thus, itis intended that the present invention covers the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

1. A method performed by a receiver to receive signals from a transmitter having a plurality of antennas, the method comprising: receiving the signals from the transmitter; selecting a precoding matrix based on a multiplexing rate (R) by selecting R column vectors from a single matrix corresponding to a maximum multiplexing rate, wherein each column vector of a first precoding matrix corresponding to a first multiplexing rate is included as a part of column vectors of a second precoding matrix corresponding to a second multiplexing rate when the second multiplexing rate is greater than the first multiplexing rate; and processing the received signals using the selected precoding matrix.
 2. The method of claim 1, wherein the maximum multiplexing rate corresponds to a number (N_(t)) of the plurality of antennas.
 3. The method of claim 2, wherein the single matrix corresponding to the maximum multiplexing rate comprises N_(t) column vectors, and wherein the selected precoding matrix comprises M column vectors selected from the N_(t) column vectors of the single matrix.
 4. The method of claim 3, wherein each column vector of the first precoding matrix is selected from the column vectors of the second precoding matrix when the second multiplexing rate is greater than the first multiplexing rate.
 5. The method of claim 1, wherein the selected precoding matrix is represented as ${P_{N_{t} \times R}^{k} = \begin{pmatrix} w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\ w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\ \vdots & \vdots & \ddots & \vdots \\ w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k} \end{pmatrix}},$ wherein w_(i,j) ^(k) (i=1, . . . , N_(t), j=1, . . . , R) denotes a complex weight value determined according to k, and k denotes a resource index, and wherein the selected precoding matrix is a unitary matrix meeting Equations A and Equations B as follows: $\begin{matrix} {{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},{{{w_{1,2}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},\vdots}{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1}} & \left\lbrack {{Equation}\mspace{14mu} A} \right\rbrack \\ {{{{{w_{1,1}^{k^{*}}w_{1,2}^{k}} + {w_{2,1}^{k^{*}}w_{2,2}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},2}^{k}}} = 0},{{{w_{1,1}^{k^{*}}w_{1,3}^{k}} + {w_{2,1}^{k^{*}}w_{2,3}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},3}^{k}}} = 0},\vdots}{{{w_{1,1}^{k^{*}}w_{1,R}^{k}} + {w_{2,1}^{k^{*}}w_{2,R}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},R}^{k}}} = 0.}} & \left\lbrack {{Equation}\mspace{14mu} B} \right\rbrack \end{matrix}$
 6. The method of claim 1, wherein the selected precoding matrix is a part of a phase shift-based precoding matrix, and wherein processing the received signals comprises using the phase shift-based precoding matrix.
 7. The method of claim 6, wherein the phase shift-based precoding matrix comprises: a diagonal matrix (D) represented as: $\begin{pmatrix} ^{j\; \theta_{1}k} & 0 & \ldots & 0 \\ 0 & ^{j\; \theta_{2}k} & \ldots & 0 \\ \vdots & \vdots & \ddots & 0 \\ 0 & 0 & \ldots & ^{j\; \theta_{N_{t}}k} \end{pmatrix},$ wherein θ_(i) denotes a phase angle for each column of the diagonal matrix (D); and a unitary matrix (U) meeting U^(H)*U=I, wherein I denotes an identity matrix.
 8. A receiving device for receiving signals from a transmitter having a plurality of antennas, the receiving device comprising: a receiver for receiving the signals from the transmitter; and a processor configured to select a precoding matrix based on a multiplexing rate (R) by selecting R column vectors from a single matrix corresponding to a maximum multiplexing rate, and to process the received signals using the selected precoding matrix, wherein each column vector of a first precoding matrix corresponding to a first multiplexing rate is included as a part of column vectors of a second precoding matrix corresponding to a second multiplexing rate when the second multiplexing rate is greater than the first multiplexing rate.
 9. The receiving device of claim 8, wherein the maximum multiplexing rate corresponds to a number (N_(t)) of the plurality of antennas.
 10. The receiving device of claim 9, wherein the single matrix corresponding to the maximum multiplexing rate comprises N_(t) column vectors, and wherein the selected precoding matrix comprises M column vectors selected from the N_(t) column vectors of the single matrix.
 11. The receiving device of claim 10, wherein each column vector of the first precoding matrix is selected from the column vectors of the second precoding matrix when the second multiplexing rate is greater than the first multiplexing rate.
 12. The receiving device of claim 8, wherein the selected precoding matrix is represented as ${P_{N_{t} \times R}^{k} = \begin{pmatrix} w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\ w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\ \vdots & \vdots & \ddots & \vdots \\ w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k} \end{pmatrix}},$ wherein w_(i,j) ^(k) (i=1, . . . , N_(t), j=1, . . . , R) denotes a complex weight value determined according to k, and k denotes an index of resource, and wherein the selected precoding matrix is a unitary matrix meeting Equations A and Equations B as follows: $\begin{matrix} {{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},{{{w_{1,2}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},\vdots}{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1}} & \left\lbrack {{Equation}\mspace{14mu} A} \right\rbrack \\ {{{{{w_{1,1}^{k^{*}}w_{1,2}^{k}} + {w_{2,1}^{k^{*}}w_{2,2}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},2}^{k}}} = 0},{{{w_{1,1}^{k^{*}}w_{1,3}^{k}} + {w_{2,1}^{k^{*}}w_{2,3}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},3}^{k}}} = 0},\vdots}{{{w_{1,1}^{k^{*}}w_{1,R}^{k}} + {w_{2,1}^{k^{*}}w_{2,R}^{k}} + \ldots + \; {w_{N_{t},1}^{k^{*}}w_{N_{t},R}^{k}}} = 0.}} & \left\lbrack {{Equation}\mspace{14mu} B} \right\rbrack \end{matrix}$
 13. The receiving device of claim 8, wherein the selected precoding matrix is a part of a phase shift-based precoding matrix, and wherein the processor processes the received signals by using the phase shift-based precoding matrix.
 14. The receiving device of claim 13, wherein the phase shift-based precoding matrix comprises: a diagonal matrix (D) represented as: $\quad\begin{pmatrix} ^{j\; \theta_{1}k} & 0 & \ldots & 0 \\ 0 & ^{j\; \theta_{2}k} & \ldots & 0 \\ \vdots & \vdots & \ddots & 0 \\ 0 & 0 & \ldots & ^{j\; \theta_{N_{t}}k} \end{pmatrix}$ wherein θ_(i) indicates a phase angle for each column of the diagonal matrix (D); and a unitary matrix (U) meeting U^(H)*U=I, wherein I denotes an identity matrix. 